The pilot was performing the third landing attempt in the light sport airplane. He reported aborting the prior attempts due to the approach being too high and fast. On the third landing, he descended to about 10 feet over the runway, when a gust of wind blew the airplane to the right, and over the taxiway. He countered with rudder and left control stick input, and the airplane returned to the runway. He allowed the airspeed to degrade, and the airplane landed hard on the nose and left wheel. The nose gear subsequently collapsed, and the airplane veered off the runway and nosed over. The airplane sustained substantial damage to the vertical stabilizer and wings during the accident sequence. The pilot reported no mechanical malfunction or failures.